with(Groebner):
with(LinearAlgebra):
T := lexdeg([x1,x2,x3],[e1,e2,e3]);
hello1 := proc(xx,yy)
return MatrixMatrixMultiply(xx,yy);
end proc:
hello2 := proc(xx,yy)
return xx+yy- MatrixMatrixMultiply(xx,yy);
end proc:
m1 := Matrix(3, 3, {(1, 1) = -.737663975994461+0.*I, (1, 2) = -.588973463383001+0.*I, (1, 3) = .330094104689369+0.*I, (2, 1) = -.588012653178741+0.*I, (2, 2) = .320157823261769+0.*I, (2, 3) = -.742792089286083+0.*I, (3, 1) = -.331802619371428+0.*I, (3, 2) = .742030476217061+0.*I, (3, 3) = .582492741708719+0.*I});
m2 := Matrix(3, 3, {(1, 1) = -.742269137704830+0.*I, (1, 2) = -.590598631673326+0.*I, (1, 3) = .316590877121441+0.*I, (2, 1) = -.593533033362923+0.*I, (2, 2) = .360143915024171+0.*I, (2, 3) = -.719732518911068+0.*I, (3, 1) = -.311054762892221+0.*I, (3, 2) = .722142379823161+0.*I, (3, 3) = .617863510611693+0.*I});
m3 := Matrix(3, 3, {(1, 1) = -.751491355856820+0.*I, (1, 2) = -.574908634018322+0.*I, (1, 3) = .323636840615627+0.*I, (2, 1) = -.575794245520782+0.*I, (2, 2) = .332066412772496+0.*I, (2, 3) = -.747123071744916+0.*I, (3, 1) = -.322058579916187+0.*I, (3, 2) = .747804760642505+0.*I, (3, 3) = .580574121936877+0.*I});
AA := hello1(m1, m2);
BB := hello2(m1, m2);
GB := Basis([e1- AA,e2- BB],T):
NormalForm(m3, GB, T);

A := `<|>`(`<,>`(1, 2,3), `<,>`(2, 3, 0), `<,>`(2, 0, 0));
v, EigenVector1:= Eigenvectors(A);
FirstEigenValue := v[1];
SecondEigenValue:= v[2];
ThirdEigenValue:= v[3];
NewMatrix3 := Matrix([[x1, x2, x3],
[x2, x3,0],
[x2,0 , 0]]);
Hello :=solve([MatrixMatrixMultiply(NewMatrix3,Matrix([[EigenVector1[1][1]],[ EigenVector1[2][1]],[ EigenVector1[3][1]]]))[1][1] = FirstEigenValue* Matrix([[EigenVector1[1][1]],[ TestPredictedProj1[2][1]],[ EigenVector1[3][1]]])[1][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[EigenVector1[1][2]],[ EigenVector1[2][2]],[ EigenVector1[3][2]]]))[2][1] = SecondEigenValue* Matrix([[EigenVector1[1][2]],[ EigenVector1[2][2]],[ EigenVector1[3][2]]])[1][1],
MatrixMatrixMultiply(NewMatrix3,Matrix([[EigenVector1[1][3]],[ EigenVector1[2][3]],[ EigenVector1[3][3]]]))[3][1] = ThirdEigenValue* Matrix([[EigenVector1[1][3]],[ EigenVector1[2][3]],[ EigenVector1[3][3]]])[1][1]
], [x1,x2,x3]);

i am confused at right hand side

 FirstEigenValue* Matrix([[EigenVector1[1][1]],[ TestPredictedProj1[2][1]],[ EigenVector1[3][1]]])[1][1]

there are three values, i do not know use which value in each equation

actually, my expectation is simple, just find back the original matrix from eigenvector and eigenvalue

Hi,

plot([[F(0,0.8)(y),y,y=0..3],[F(0.1,0.8)(y),y,y=0..3],[F(0.2,0.8)(y),y,y=0..3]],numpoints=25,color=[red,green,blue],view=[-0.3..0.5,0..2.5]);

p1:=%:

data:=plottools:-getdata~([p1]):

dm1:=op([1,-1],data);

              dm1 := Vector(4, {(1) = ` 36 x 2 `*Matrix,

                        (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})

dm2:=op([2,-1],data);

           dm2 := Vector(4, {(1) = ` 32 x 2 `*Matrix,

                    (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})

dm3:=op([3,-1],data);

                       dm3 := Vector(4, {(1) = ` 28 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage:                                         `*rectangular, (4) = `Order: `*Fortran_order})

How to combine these three matrices into a single one with four columns (y, F(0,0.8)(y), F(0.1,0.8)(y), F(0.2,0.8)(y) )?

Thanks

I  get  this  from  pdsolve as a  "solution"

p[42] := -Pi+.2+3.0*x+3.2*t+2*Intat(2.25*_f/sqrt(-1.5*_f*(-1.6+4.0500*_f^2+3.7125*_f)), _f = 0)

it does not eval to anything, what is this ?

Dear Maple users

My question is probably simple, but I can't seem to figure out how to do it in a smart way way without using procedures: My task is to create a cumulative list from a list. Ex: From [3,-2,5,1,10,7] I want to create the list [3,1,6,7,17,24]. Every entrance in the new list is the sum of the previous ones including the actual entrance. The Statistics package contain a command named CumulativeSum, but unfortunately a list is not returned ... I hope someone can help doing it is a simple way.

Regards,

Erik

Hi,

I'm trying to plot a function that contains an integral. I was finding that the plots seem to take far too long to make. When I just evaluate the function at a given point it computes almost instantly. So I tried setting setting adaptive plotting off and setting numpoints=5. This provides a plot very quickly (a few seconds) but if I raise the number of points up to 10 it runs indefinitely (I stopped it after 15 minutes). Could there be something else going on here? Does plot still evaluate at more than numpoints sometimes even if adaptive plotting is turned off?

Perhaps I am being blind, but I cannot locate a function for performing the direct sum of two (or more, for that matter) matrices, i.e., constructing a new matrix with the two (or more) matrices arranged block-diagonally.

Such a function should, I guess, naturally accompany the function KroneckerProduct in the LinearAlgebra package, because direct products (Kronecker products) of representations (i.e., matrrix-valued realizations of some abstract algebra) are, as is well-known, generally reducible into a direct sum of irreducible subrepresentations.

Hi

I have been trying to find a way to present results from engineering calcs to 2 decimal places (i.e.: 350.50) but the round function rounds to the nearest integer. Is there a specific statement for specifying the number of decimal places you want to present some results?

thanks

> assume(a < 0);
> convert(cosh(sqrt(a)), sincos);
print(`output redirected...`); # input placeholder
/ (1/2)\
cos\(-a) /

This is what I expected.

Now

> assume(L > 0);
> assume(K > 0);
> assume(mu > 0);
> assume(mu^2 < 4*L*k);
> assume(t > 0);
> convert(cosh((1/2)*t*sqrt(mu^2-4*L*k)/L), sincos);
print(`output redirected...`); # input placeholder
/ (1/2)\
| / 2 \ |
|t \mu - 4 L k/ |
cosh|--------------------|
\ 2 L /

I wanted to obtain again the cos function. Could someone help me?
(What is the reason that convert does not work "well" in later case?)

 Thanks,  Sandor

Dear guys

I have a function as P(t)=t*ln(t)^(-b) and I know that V(P)=P^(-2). I want to plot Vwith respect to for example Q.

All the things I know about Q is it is a function of t as well and diff(P(t),t) = diff(Q(t),t)^2.

How can I plot V with respec to Q?

Thanks a lot. 

Hi,

I tried to create a graph with two different x-axes and y-axes, for example:

It's no doubt that we can use the "dualaxisplot" to generated a plot with two different y-axes as follows:

It's seem that Maple can realize plots with two different x-axes , because some of cases present functions through upper x-axis, such as:

How should I create a graph to display functions using the bottom and left sides as the x- and y-axis for one, and the top and right sides as the x- and y-axis for the other?

I'd appreciate any help on this topic. Thank a lot.

Please

can someone tell me how to plot values directly from an array? I'd have thought that this was a simple task but unfortunately I havent seen any useful examples in the Maple Help.

Let's say any array such as A:=Array(1..4,1..4); with random numbers.

I want to plot column 1 vs 3, how do I do it?

thanks

Hello.

Could not evaluate numerical integral with constant in it. I use method = _cuhre.  Maple print solution like this:

Int(Int(Int(max(0., (0.9483573506e-3*(-1.*sin(a)*cos(w)-1.*cos(a)*sin(w)*sin(b)))*cos(a)*cos(b)^2*(-58.5*signum(cos(b)*sin(w)*sin(b))*kk+200.*cos(b)*sin(w)*sin(b))*Heaviside(-58.5+200.*cos(b)*sin(w)*sin(b)*signum(cos(b)*sin(w)*sin(b))*kk)*Heaviside(1.-.98*cos(b)^2)/sqrt(1.-.98*cos(b)^2)), a = 0. .. 6.283185308), b = 0. .. 1.570796327), w = 0. .. 6.283185308)+Int(Int(Int(min(0., (0.9483573506e-3*(-1.*sin(a)*cos(w)-1.*cos(a)*sin(w)*sin(b)))*cos(a)*cos(b)^2*(-58.5*signum(cos(b)*sin(w)*sin(b))*kk+200.*cos(b)*sin(w)*sin(b))*Heaviside(-58.5+200.*cos(b)*sin(w)*sin(b)*signum(cos(b)*sin(w)*sin(b))*kk)*Heaviside(1.-.98*cos(b)^2)/sqrt(1.-.98*cos(b)^2)), a = 0. .. 6.283185308), b = 0. .. 1.570796327), w = 0. .. 6.283185308)

How could it be taken.

Thank!!!

Does anyone exports Maple worksheets to as a LaTeX file?

All my work is typed in LaTeX but I rarely export a Maple file as LaTeX because Maple uses its own LaTeX macros that in a generous evaluation are a lot of "junk" around the LaTeX code. In practice  it is is easier to copy and past the Maple output and then make modifications to LaTeX by hand than to modify Maple's LaTeX code.

Does anyone know of a more efficient alternative than manually copying and pasting?

The ability to export LaTeX useful LaTeX code should be a basic to any symbolic math software, this is one of the few feature os Maple that are really disappointing.

i have got alot of mixed and high degree derivatives. For example:

u[x]*u[x,t]*eta[x,t]+u[]^2*u[x]*eta[x]+kis(x,y)u[x,t]^2*u[]+eta(x, y)*u[]*u[x]^2+ksi[x,t]*u[x]^2*u[x,t]+......

like this alot of terms

my question is how can i solve divided by the derivative of the u(x,t) partial differential equations system and so  how can i find eta(x,t,u) and ksi(x,t,u)